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Foundations of Quantum Physics II. the Thermal Interpretation Foundations of quantum physics II. The thermal interpretation Arnold Neumaier Fakult¨at f¨ur Mathematik, Universit¨at Wien Oskar-Morgenstern-Platz 1, A-1090 Wien, Austria email: [email protected] http://www.mat.univie.ac.at/~neum April 24, 2019 Abstract. This paper presents the thermal interpretation of quantum physics. The in- sight from Part I of this series that Born’s rule has its limitations – hence cannot be the foundation of quantum physics – opens the way for an alternative interpretation: the ther- mal interpretation of quantum physics. It gives new foundations that connect quantum physics (including quantum mechanics, statistical mechanics, quantum field theory and their applications) to experiment. The thermal interpretation resolves the problems of the foundations of quantum physics revealed in the critique from Part I. It improves the traditional foundations in several respects: The thermal interpretation reflects the actual practice of quantum physics, especially • regarding its macroscopic implications. The thermal interpretation gives a fair account of the interpretational differences between quantum• mechanics and quantum field theory. The thermal interpretation gives a natural, realistic meaning to the standard formalism of• quantum mechanics and quantum field theory in a single world, without introducing additional hidden variables. The thermal interpretation is independent of the measurement problem. The latter • arXiv:1902.10779v2 [quant-ph] 24 Apr 2019 becomes a precise problem in statistical mechanics rather than a fuzzy and problematic notion in the foundations. Details will be discussed in Part III. For the discussion of questions related to this paper, please use the discussion forum https://www.physicsoverflow.org. 1 Contents 1 Introduction 3 2 The thermal interpretation of quantum mechanics 5 2.1 The Ehrenfest picture of quantum mechanics . .... 5 2.2 Properties ..................................... 8 2.3 Uncertainty .................................... 10 2.4 Whatisanensemble?............................... 12 2.5 Formal definition of the thermal interpretation . ..... 14 3 Thermal interpretation of statistics and probability 17 3.1 Classical probability via expectation . 17 3.2 Description dependence of probabilities . .. 21 3.3 Deterministic and stochastic aspects . .. 23 3.4 Whatisprobability? ............................... 26 3.5 Probabilitymeasurements ............................ 28 3.6 The stochastic description of a deterministic system . ..... 29 4 The thermal interpretation of quantum field theory 30 4.1 Beables and observability in quantum field theory . .. 31 4.2 Dynamicsinquantumfieldtheory. 33 4.3 Theuniverseasaquantumsystem . 34 4.4 Relativistic causality . 36 4.5 Nonlocal correlations and conditional information . .... 37 5 Conclusion 39 References 40 2 1 Introduction In a statistical description of nature only expectation values or correla- tions are observable. Christof Wetterich, 1997 [57] One is almost tempted to assert that the usual interpretation in terms of sharp eigenvalues is ’wrong’, because it cannot be consistently main- tained, while the interpretation in terms of expectation values is ’right’, because it can be consistently maintained. John Klauder, 1997 [26, p.6] This paper presents the thermal interpretation of quantum physics. The insight from Part I [38] of this series was that Born’s rule has its limitations and hence cannot be the foundation of quantum physics. Indeed, a foundation that starts with idealized concepts of limited validity is not a safe ground for interpreting reality. The analysis of Part I opens the way for an alternative interpretation – the thermal in- terpretation of quantum physics. It gives new foundations that connect all of quantum physics (including quantum mechanics, statistical mechanics, quantum field theory and their applications) to experiment. Quantum physics, as it is used in practice, does much more than predicting probabilities for the possible results of microscopic experiments. This introductory textbook scope is only the tip of an iceberg. Quantum physics is used to determine the behavior of materials made of specific molecules under changes of pressure or temperature, their response to external electromagnetic fields (e.g., their color), the production of energy from nuclear reactions, the behavior of transistors in the microchips on which modern computers run, and a lot more. Indeed, it appears to predict the whole of macroscopic, phenomenological equilibrium and nonequilibrium thermodynamics in a quantitatively correct way. Motivated by this fact, this paper defines and discusses a new interpretation of quantum physics, called the thermal interpretation. It is based on the lack of a definite boundary between the macroscopic and the microscopic regime, and an application of Ockham’s razor [44, 24], frustra fit per plura quod potest fieri per pauciora – that we should opt for the most economic model explaining a regularity. Essential use is made of the fact that everything physicists measure is measured in a ther- mal environment for which statistical thermodynamics is relevant. This is reflected in the characterizing adjective ’thermal’ for the interpretation. The thermal interpretation agrees with how one interprets measurements in thermodynamics, the macroscopic part of quan- tum physics, derived via statistical mechanics. Extrapolating from the macroscopic case, the thermal interpretation considers the functions of the state (or of the parameters charac- terizing a state from a particular family of states) as the beables, the conceptual equivalent of objective properties of what really exists. Some of these are accessible to experiment – namely the expectation values of quantities that have a small uncertainty and vary suffi- ciently slowly in time and space. Because of the law of large numbers, all thermodynamic 3 variables are in this category. By its very construction, the thermal interpretation naturally matches the classical properties of our quantum world. Section2 gives a detailed motivation of the thermal interpretation and a precise definiton of its basic credo. We introduce the Ehrenfest picture of quantum mechanics, the abstract mathematical framework used throughout. It describes a closed, deterministic dynamics for q-expectations (expectation values of Hermitian operators). We discuss the ontological status of the thermal interpretation, making precise the concept of properties of a quantum system, the concept of uncertainty, and the notion of an ensemble. Based on this, we give a formal definition of the thermal interpretation, In Section 3 we consider the way the thermal interpretation represents statistical and prob- abilistic aspects of quantum theory. We begin with a discussion of two formal notions of classical probability, their relation to the probability concept used in applied statistics, and their dependence on the description used. We then show how the statistical aspects of the quantum formalism naturally follow from the weak law of large numbers. In Section 4, we show that the fact that in relativistic quantum field theory, position is a classical parameter while in quantum mechanics it is an uncertain quantity strongly affects the relation between quantum field theory and reality. Among the beables of quantum field theory are smeared field expectations and pair correlation functions, which encode most of what is of experimental relevance in quantum field theory. We discuss notions of causality and nonlocality and their relation to the thermal interpretation. We also discuss relativistic quantum field theory at finite times, a usually much neglected topic essential for a realistic interpretation of the universe in terms of quantum field theory. According to the thermal interpretation, quantum physics is the basic framework for the description of objective reality (including everything reproducible studied in experimental physics), from the smallest to the largest scales, including the universe as a whole (cf. Subsection 4.3). Classical descriptions are just regarded as limiting cases where Planck’s constanth ¯ can be set to zero without significant loss of quality of the resulting models. Except for a brief discussion of the measurement of probabilities in Subsection 3.5, every- thing related to the thermal interpretation of measurement is postponed to Part III [39] of this series of papers. There it is shown that the thermal interpretation satisfactorily re- solves the main stumbling blocks in a clear description of the relation between the quantum formalism and experimental reality. Hints at a possible thermal interpretation of quantum physics go back at least to 1997; see the above quotes by Wetterich and Klauder. A recent view closely related to the thermal interpretation is the 2017 work by Allahverdyan et al. [1]. The thermal interpretation of quantum physics itself emerged from my foundational 2003 paper Neumaier [32]. It was developed by me in discussions on the newsgroups de.sci.physik, starting in Spring 2004; for the beginnings see Neumaier [34]. A first version of it was fully formalized (without naming the interpretation) in Sections 5.1, 5.4 and Chapter 7 of the 2008 edition of the online book by Neumaier & Westra [41]; see also Sections 8.1, 8.4 and Chapter 10 of the 2011 edition. The name ’thermal interpretation’ appeared first in a 2010 lecture (Neumaier [35]). Later I created a dedicated website on the topic (Neumaier [37]). 4 The bulk of this paper is intended to be nontechnical and understandable
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